In seismic exploration, a seismic energy-source transducer injects a seismic signal into the earth. The signal travels downwardly and becomes reflected from subsurface formations. The reflected signal returns to the surface of the earth where it is detected by sensitive geophones which convert the reflected seismic signals to electrical signals and transmit the signals to a signal utilization device. The traveltime delay between the time of injection of the original seismic signal and the time of reception of the reflected signals by the geophones is a function of the depth of the respective formations. Typically, a maximum reflection-time delay on the order of several seconds is expected, while reflections from shallower formations will arrive proportionately sooner.
In one method of seismic exploration, the seismic energy source transducer produces a sweep signal. The sweep signal is a unique wave train that is nonrepetitive during a period which is at least as long as the maximum traveltime delay. The sweep-signal wave train will be reflected from several subsurface formations. Seismic signals received by the geophones will be a complex wave train containing successively overlapping images of the original sweep signal. The beginning of each of the overlapping images will be shifted in time from the instant of initiation of the sweep signal in proportion to the vertical depth of the formations.
Useful information from the complex, reflected wave train is obtained by serially correlating that wave train with a replica of the original sweep signal. From the results of serial correlation, a correlogram can be constructed. The time delays to successive correlogram peaks are functions of the depths of each reflector. Methods and apparatus for practicing this technique of seismic exploration are very well known to the art; see for example, U.S. Pat. No. 2,688,124.
Generally, reflection signals produced by the use of such sweep signals are so weak that many must be added together to produce a legible product. It is also commonplace to effect much of the adding process in the field to avoid the expense of separately recording and storing the result of the application of each individual sweep signal. Correlation in the prior art has customarily taken place after the so-called "vertical" summing and prior to the so-called "horizontal" summing.
Side lobes, especially those attendant upon refraction signals and upon particularly strong reflection signals, were an unwelcome by-product of the correlation process. The side lobes were added in phase (i.e., coherently) by the vertical stacking process and at least in part by the horizontal stacking process.
It has long been recognized that it would be desirable to effect correlation before all of the adding or stacking processes, if an adequate field correlator could be made available and if the side lobes could somehow be suppressed. Unfortunately, in the prior art the only recognized but uneconomical method of suppressing side lobes was to increase the length of the operator.
Seismic data are customarily expressed, recorded, and manipulated as binary numbers with a typical resolution of 15 bits plus a sign bit. A typical reflected time series may have a 24-second duration and a 4ms sample rate. Therefore, a conventional field correlator may require storage for 6000 16-bit data samples for the reflected data. A memory for 3000 16-bit samples may be needed to store the original 12-second sweep signal, and an additional 3000 32-bit locations may be needed as a buffer storage for the integrated cross products. It is apparent, therefore, that a tremendous amount of bulk digital storage is needed to handle the correlation computations.
Large digital computers equipped with array processors, such as are found in a central data-processing center, can handle serial-correlation problems without difficulty. For a field correlator, however, the physical size of the required bulk storage, the expense of the hardware, and field time lost in making the computations requiring manipulation of 16- and 32- bit numbers render present state-of-the-art field correlators either complicated, expensive, or very slow. Alternative prior-art field correlators use crude approximations, typically only 4 or 8 bits of the 16-bit seismic and sweep-data words, in order to reduce the storage requirements. But, the resulting correlograms lack resolution.
Approximation by use of such truncated data words is of the so-called constant absolute error type. It is damaging to the resulting, desired, output signals and severely restricts the dynamic range of the entire seismograph record. What was needed was a method of approximation with a constant relative error so as to be useful over the entire dynamic range of seismograph signals.
Seismic data are recorded on magnetic tape in the field as digital, floating-point, computer-compatible numbers. A floating-point number includes an algebraic sign, an exponent to a selected number base, and a mantissa. Before these numbers can be processed by conventional field correlators, it is necessary to normalize the floating-point numbers to fixed-point binary integers. The hardware needed for such normalization is complicated and expensive; furthermore, the field-correlator's computation-time is necessarily increased.
There is a need, therefore, for a fast serial correlation method for field use that will be of constant relative error type, that requires inexpensive, compact hardware, that reduces the size of the required data-storage capacity, simplifies the arithmetic, and eliminates the need for conversion of floating-point numbers to integers.